1. Field of the Invention.
The present invention relates to a method and means for evaluating phase encoded communication systems and, more particularly, to a method and means for determining the probability density function associated with transition displacements of a data signal encoded with a known format.
2. Description of the Prior Art.
Conventional data handling systems usually require input digital data to be phase encoded in accordance with the standard non-return-to-zero (NRZ) format. In the NRZ format, a "0" is represented by an output signal at a first voltage level and a "1" is represented by an output signal at a second, higher voltage level. Since several bit cells may occur without a transition of the data from one voltage level to the other, NRZ encoded data is usually accompanied by a coherent clock signal which defines the boundaries of the bit cells.
When transmitting serial digital data over a data communication network, it is desirable to encode such data in accordance with a self-clocking format so that a separate clock signal need not be transmitted. Elimination of the separate clock signal eliminates the necessity for an additional communications channel.
Many self-clocking codes are presently in existence and are widely used. Self-clocking codes are those in which transitions are caused to occur with a regularity sufficient to limit the d.c. spectral content of the encoded signal and to provide timing information for clock reconstruction. In other words, in all self-clocking codes, the information to be transmitted is contained, not only in the level of the waveform but, additionally, in the time of occurrence of the transition from one level to the other. The most popular self-clocking codes can be considered as either bi-phase or double density. However, other self-clocking codes exist.
Where digital data, which is encoded in accordance with a self-clocking format, is transmitted over a communications channel to eliminate the necessity for transmitting a separate clock signal, it becomes necessary, at the receiving location, to convert the data to its NRZ format equivalent for application to a shift register or other data handling system. It is also necessary to generate a coherent clock signal to define the boundaries of the bit cells. Apparatus for converting serial digital data which is phase encoded in accordance with any self-clocking format to its NRZ format equivalent accompanied by a coherent clock signal is known to those skilled in the art.
Practical digital communications channels and digital recording systems in particular, are both bandwidth limited and noisy. Bandwidth limiting results in a phenomenon referred to as intersymbol interference in which the symbols of the data format become smeared in time and tend to overlap. The result of this process is manifested as data dependent amplitude and phase distortions. The noise present on the channel may further corrupt the amplitude and phase of the signal. Since it is common practice to remove the amplitude variations of the received or reproduced data by limiting techniques, the overall effect of intersymbol interference and noise is most commonly manifested as random displacements (jitter) of the data transitions. Should a displacement occur beyond the limits of the receiving station to absorb, such displaced transition may cause the receiving station decoder to incorrectly decode the data, producing an error.
When designing a communications system, it is very difficult to predict what the error rate will be. Therefore, once a system is designed and it becomes necessary to find out how good it is, about the only thing that can be done is to test the system and determine its error rate. If the system is designed properly, as a practical matter, it will operate below the threshold of error most of the time. Therefore, a measurement of errors alone often gives no information as to how much margin there is against a wrong decision. In other words, the decoder has certain limits and an error will only be indicated when a transition is sufficiently displaced to go beyond the boundaries of the decoder. If transitions are in fact being displaced but are not sufficiently displaced to go beyond the boundaries of the decoder, then the decoder does not communicate that an error has occurred. Therefore, no useful information as to the margin against an error is provided.
In general, the measurement of data signal distortion involves the measurement of the time displacement of the signal transitions from their normal undistorted positions. A variety of techniques have been developed for making such a measurement. However, many of such systems operate on assumptions which prove, in practice, to be invalid. For example, some systems operate on the assumption that phase error can be characterized as a Gaussian distributed random variable and such an assumption, in many cases, is unwarranted. Accordingly, the assessment of system performance based on such an assumption may well lead to an erroneous conclusion.
Many methods of signal analysis are based on oscilloscope displays. In every case, however, the measurements are limited by the persistence of the scope phosphor and human contrast perception and these are severely limiting factors.
Still other systems restrict the input data to a fixed frequency. Since that jitter occurring as the result of intersymbol interference can be evaluated only when the data is permitted to assume all possible encoded states, the contribution of intersymbol interference to the overall displacement of transitions is clearly not measurable if the frequency of the data is arbitrarily fixed.